Optimal. Leaf size=105 \[ \frac {1215}{896} (1-2 x)^{21/2}-\frac {59049 (1-2 x)^{19/2}}{2432}+\frac {409941 (1-2 x)^{17/2}}{2176}-\frac {105399}{128} (1-2 x)^{15/2}+\frac {3658095 (1-2 x)^{13/2}}{1664}-\frac {5078115 (1-2 x)^{11/2}}{1408}+\frac {3916031 (1-2 x)^{9/2}}{1152}-\frac {184877}{128} (1-2 x)^{7/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 105, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ \frac {1215}{896} (1-2 x)^{21/2}-\frac {59049 (1-2 x)^{19/2}}{2432}+\frac {409941 (1-2 x)^{17/2}}{2176}-\frac {105399}{128} (1-2 x)^{15/2}+\frac {3658095 (1-2 x)^{13/2}}{1664}-\frac {5078115 (1-2 x)^{11/2}}{1408}+\frac {3916031 (1-2 x)^{9/2}}{1152}-\frac {184877}{128} (1-2 x)^{7/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^{5/2} (2+3 x)^6 (3+5 x) \, dx &=\int \left (\frac {1294139}{128} (1-2 x)^{5/2}-\frac {3916031}{128} (1-2 x)^{7/2}+\frac {5078115}{128} (1-2 x)^{9/2}-\frac {3658095}{128} (1-2 x)^{11/2}+\frac {1580985}{128} (1-2 x)^{13/2}-\frac {409941}{128} (1-2 x)^{15/2}+\frac {59049}{128} (1-2 x)^{17/2}-\frac {3645}{128} (1-2 x)^{19/2}\right ) \, dx\\ &=-\frac {184877}{128} (1-2 x)^{7/2}+\frac {3916031 (1-2 x)^{9/2}}{1152}-\frac {5078115 (1-2 x)^{11/2}}{1408}+\frac {3658095 (1-2 x)^{13/2}}{1664}-\frac {105399}{128} (1-2 x)^{15/2}+\frac {409941 (1-2 x)^{17/2}}{2176}-\frac {59049 (1-2 x)^{19/2}}{2432}+\frac {1215}{896} (1-2 x)^{21/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 48, normalized size = 0.46 \[ -\frac {(1-2 x)^{7/2} \left (505076715 x^7+2753997246 x^6+6628858236 x^5+9228315096 x^4+8157896208 x^3+4700947104 x^2+1706820416 x+323646080\right )}{2909907} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.96, size = 59, normalized size = 0.56 \[ \frac {1}{2909907} \, {\left (4040613720 \, x^{10} + 15971057388 \, x^{9} + 23013359226 \, x^{8} + 10299128697 \, x^{7} - 8457459318 \, x^{6} - 11546145324 \, x^{5} - 3037739768 \, x^{4} + 2155110064 \, x^{3} + 1656222432 \, x^{2} + 235056064 \, x - 323646080\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.07, size = 129, normalized size = 1.23 \[ \frac {1215}{896} \, {\left (2 \, x - 1\right )}^{10} \sqrt {-2 \, x + 1} + \frac {59049}{2432} \, {\left (2 \, x - 1\right )}^{9} \sqrt {-2 \, x + 1} + \frac {409941}{2176} \, {\left (2 \, x - 1\right )}^{8} \sqrt {-2 \, x + 1} + \frac {105399}{128} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} + \frac {3658095}{1664} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} + \frac {5078115}{1408} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {3916031}{1152} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {184877}{128} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 45, normalized size = 0.43 \[ -\frac {\left (505076715 x^{7}+2753997246 x^{6}+6628858236 x^{5}+9228315096 x^{4}+8157896208 x^{3}+4700947104 x^{2}+1706820416 x +323646080\right ) \left (-2 x +1\right )^{\frac {7}{2}}}{2909907} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 73, normalized size = 0.70 \[ \frac {1215}{896} \, {\left (-2 \, x + 1\right )}^{\frac {21}{2}} - \frac {59049}{2432} \, {\left (-2 \, x + 1\right )}^{\frac {19}{2}} + \frac {409941}{2176} \, {\left (-2 \, x + 1\right )}^{\frac {17}{2}} - \frac {105399}{128} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} + \frac {3658095}{1664} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} - \frac {5078115}{1408} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {3916031}{1152} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {184877}{128} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 73, normalized size = 0.70 \[ \frac {3916031\,{\left (1-2\,x\right )}^{9/2}}{1152}-\frac {184877\,{\left (1-2\,x\right )}^{7/2}}{128}-\frac {5078115\,{\left (1-2\,x\right )}^{11/2}}{1408}+\frac {3658095\,{\left (1-2\,x\right )}^{13/2}}{1664}-\frac {105399\,{\left (1-2\,x\right )}^{15/2}}{128}+\frac {409941\,{\left (1-2\,x\right )}^{17/2}}{2176}-\frac {59049\,{\left (1-2\,x\right )}^{19/2}}{2432}+\frac {1215\,{\left (1-2\,x\right )}^{21/2}}{896} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 31.07, size = 94, normalized size = 0.90 \[ \frac {1215 \left (1 - 2 x\right )^{\frac {21}{2}}}{896} - \frac {59049 \left (1 - 2 x\right )^{\frac {19}{2}}}{2432} + \frac {409941 \left (1 - 2 x\right )^{\frac {17}{2}}}{2176} - \frac {105399 \left (1 - 2 x\right )^{\frac {15}{2}}}{128} + \frac {3658095 \left (1 - 2 x\right )^{\frac {13}{2}}}{1664} - \frac {5078115 \left (1 - 2 x\right )^{\frac {11}{2}}}{1408} + \frac {3916031 \left (1 - 2 x\right )^{\frac {9}{2}}}{1152} - \frac {184877 \left (1 - 2 x\right )^{\frac {7}{2}}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________